2010004809
Level:
C
Evaluate the following expression at \(x = 9\).
\[
\frac{x^{-2}}
{x^{-\frac{1}{2}} - x^{-1}}
\]
\(\frac{1}
{18}\)
\(-\frac{1}
{18} \)
\(\frac{27}
{2}\)
\(-\frac{27}
{8}\)
C
2000006804
Level:
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given inequalities. Which of the inequalities is it?
\[\begin{aligned}
y &\leq x
\\y &\geq -x
\end{aligned}\]
\[\begin{aligned}
y &\leq - x
\\y &\geq x
\end{aligned}\]
\[\begin{aligned}
y &\leq x
\\y &\leq -x
\end{aligned}\]
\[\begin{aligned}
y &\geq x
\\y &\geq -x
\end{aligned}\]
2000006803
Level:
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given inequalities. Which of the inequality is it?
\[\begin{aligned}
y &\leq x+2
\\y &\geq x -2
\end{aligned}\]
\[\begin{aligned}
y &\leq x-2
\\y &\geq x+2
\end{aligned}\]
\[\begin{aligned}
y &\leq 2x+2
\\y &\geq 2x -2
\end{aligned}\]
\[\begin{aligned}
y &\leq 2x-2
\\y &\geq 2x +2
\end{aligned}\]
2000006802
Level:
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given inequalities. Which of the inequality is it?
\(y \leq -2x\)
\(y \geq -2x\)
\(y \leq -\frac{x}2\)
\(y \geq -\frac{x}2\)
2000006801
Level:
C
In the picture, the shaded region corresponds to the set of points that is the solution to one of the given inequalities. Which of the inequalities is it?
\(y \geq x+1\)
\(y \geq x-1\)
\(y \leq x+1\)
\(y \leq x-1\)
2000006512
Level:
C
Let \(ABCDV\) be a rectangle based-pyramid, where \(V\) is its apex and \(L\), \(N\) are the midpoints of its edges \(BC\), \(CV\) respectively. What is the cross-section of the pyramid if we slice it with a plane \(ALN\)?
a quadrilateral \(ALNR\) with point \(R\) lying on the edge \(DV\)
a triangle \(ALN\)
a quadrilateral \(ALNR\) with point \(R\) lying on the edge \(AV\)
a quadrilateral \(ALNR\) with point \(R\) lying on the edge \(BV\)
2000006511
Level:
C
Let \(ABCDV\) be a rectangle based-pyramid, where \(V\) is its apex and \(K\), \(M\) are the midpoints of its edges \(AD\), \(BV\) respectively. What is the cross-section of the pyramid if we slice it with a plane \(KCM\)?
a quadrilateral \(KCMP\) with point \(P\) lying on the edge \(AV\)
a triangle \(KCM\)
a quadrilateral \(KCMP\) with point \(P\) lying on the edge \(DV\)
a quadrilateral \(KCMP\) with point \(P\) lying on the median \(KV\) if the triangle \(ADV\)
2000006506
Level:
C
Let \( ABCDEFGH \) be a cube with \( K \) and \( L \) being the midpoints of edges \( AB \) and \( BC \) respectively, and let \( M \) be the centre of its lateral face \( ADHE \). What is the cross-section of the cube if we slice it with a plane \( KLM \)?
a pentagon \( KLPQR \) with points \( P \), \( Q \), and \( R \) lying on edges \( CG \), \( DH \), and \( AE \) respectively
a triangle \( KLM \)
a pentagon \( KLPQM \) with points \( P \) and \( Q \) lying on edges \( CG \) and \( DH \) respectively
a quadrilateral \( KLMR \) with point \( R \) lying on the edge \( AE \)
2000006505
Level:
C
Let \( ABCDV \) be a rectangle based-pyramid, where \( V \) is its apex and \( K \), \( L \), \( M \), and \(N\) are the midpoints of its edges \( AD \), \( BC \), \(BV\), and \( CV \) respectively. What is the mutual position of planes \( KCM \) and \( ALN \)?
intersecting planes
distinct parallel planes
identical planes
2000006008
Level:
C
The trapezoid \(KLMN\) has bases \(15\,\mathrm{cm}\) and \(10\,\mathrm{cm}\) long. The point \(T\) is any point of the longer base. The area of the triangle \(MNT\) is \(40\,\mathrm{cm}^2\). What is the area of the trapezoid \(KLMN\)?
\(100\,\mathrm{cm}^2\)
\(80\,\mathrm{cm}^2\)
\(120\,\mathrm{cm}^2\)
\(50\,\mathrm{cm}^2\)